Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 74.5% → 83.0%

Time: 39.0s

Alternatives: 22

Speedup: 0.5×

• 56.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
  (* j (- (* c t) (* i y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
  (* j (- (* c t) (* i y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 83.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
          (* j (- (* t c) (* y i))))))
   (if (<= t_1 INFINITY) t_1 (* i (- (* a b) (* y j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = i * ((a * b) - (y * j));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = i * ((a * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = i * ((a * b) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = i * ((a * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 87.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 57.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 57.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 57.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   5. Simplified 57.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 65.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_4 := t\_3 - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{if}\;i \leq -2.2 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t\_3\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -7.7 \cdot 10^{+15}:\\ \;\;\;\;t\_2 + t\_3\\ \mathbf{elif}\;i \leq -7.6 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -4.5 \cdot 10^{-171}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{-24}:\\ \;\;\;\;\left(t\_2 - x \cdot \left(t \cdot a - y \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{+131}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a)))))
        (t_2 (* c (* t j)))
        (t_3 (* b (- (* a i) (* z c))))
        (t_4 (- t_3 (* j (- (* y i) (* t c))))))
   (if (<= i -2.2e+152)
     (+ (* y (- (* x z) (* i j))) t_3)
     (if (<= i -1.05e+91)
       t_1
       (if (<= i -7.7e+15)
         (+ t_2 t_3)
         (if (<= i -7.6e-91)
           t_1
           (if (<= i -4.5e-171)
             t_4
             (if (<= i 1.15e-24)
               (- (- t_2 (* x (- (* t a) (* y z)))) (* b (* z c)))
               (if (<= i 4.8e+131) t_4 (* i (- (* a b) (* y j))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double t_2 = c * (t * j);
	double t_3 = b * ((a * i) - (z * c));
	double t_4 = t_3 - (j * ((y * i) - (t * c)));
	double tmp;
	if (i <= -2.2e+152) {
		tmp = (y * ((x * z) - (i * j))) + t_3;
	} else if (i <= -1.05e+91) {
		tmp = t_1;
	} else if (i <= -7.7e+15) {
		tmp = t_2 + t_3;
	} else if (i <= -7.6e-91) {
		tmp = t_1;
	} else if (i <= -4.5e-171) {
		tmp = t_4;
	} else if (i <= 1.15e-24) {
		tmp = (t_2 - (x * ((t * a) - (y * z)))) - (b * (z * c));
	} else if (i <= 4.8e+131) {
		tmp = t_4;
	} else {
		tmp = i * ((a * b) - (y * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
    t_2 = c * (t * j)
    t_3 = b * ((a * i) - (z * c))
    t_4 = t_3 - (j * ((y * i) - (t * c)))
    if (i <= (-2.2d+152)) then
        tmp = (y * ((x * z) - (i * j))) + t_3
    else if (i <= (-1.05d+91)) then
        tmp = t_1
    else if (i <= (-7.7d+15)) then
        tmp = t_2 + t_3
    else if (i <= (-7.6d-91)) then
        tmp = t_1
    else if (i <= (-4.5d-171)) then
        tmp = t_4
    else if (i <= 1.15d-24) then
        tmp = (t_2 - (x * ((t * a) - (y * z)))) - (b * (z * c))
    else if (i <= 4.8d+131) then
        tmp = t_4
    else
        tmp = i * ((a * b) - (y * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double t_2 = c * (t * j);
	double t_3 = b * ((a * i) - (z * c));
	double t_4 = t_3 - (j * ((y * i) - (t * c)));
	double tmp;
	if (i <= -2.2e+152) {
		tmp = (y * ((x * z) - (i * j))) + t_3;
	} else if (i <= -1.05e+91) {
		tmp = t_1;
	} else if (i <= -7.7e+15) {
		tmp = t_2 + t_3;
	} else if (i <= -7.6e-91) {
		tmp = t_1;
	} else if (i <= -4.5e-171) {
		tmp = t_4;
	} else if (i <= 1.15e-24) {
		tmp = (t_2 - (x * ((t * a) - (y * z)))) - (b * (z * c));
	} else if (i <= 4.8e+131) {
		tmp = t_4;
	} else {
		tmp = i * ((a * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	t_2 = c * (t * j)
	t_3 = b * ((a * i) - (z * c))
	t_4 = t_3 - (j * ((y * i) - (t * c)))
	tmp = 0
	if i <= -2.2e+152:
		tmp = (y * ((x * z) - (i * j))) + t_3
	elif i <= -1.05e+91:
		tmp = t_1
	elif i <= -7.7e+15:
		tmp = t_2 + t_3
	elif i <= -7.6e-91:
		tmp = t_1
	elif i <= -4.5e-171:
		tmp = t_4
	elif i <= 1.15e-24:
		tmp = (t_2 - (x * ((t * a) - (y * z)))) - (b * (z * c))
	elif i <= 4.8e+131:
		tmp = t_4
	else:
		tmp = i * ((a * b) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))))
	t_2 = Float64(c * Float64(t * j))
	t_3 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_4 = Float64(t_3 - Float64(j * Float64(Float64(y * i) - Float64(t * c))))
	tmp = 0.0
	if (i <= -2.2e+152)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + t_3);
	elseif (i <= -1.05e+91)
		tmp = t_1;
	elseif (i <= -7.7e+15)
		tmp = Float64(t_2 + t_3);
	elseif (i <= -7.6e-91)
		tmp = t_1;
	elseif (i <= -4.5e-171)
		tmp = t_4;
	elseif (i <= 1.15e-24)
		tmp = Float64(Float64(t_2 - Float64(x * Float64(Float64(t * a) - Float64(y * z)))) - Float64(b * Float64(z * c)));
	elseif (i <= 4.8e+131)
		tmp = t_4;
	else
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	t_2 = c * (t * j);
	t_3 = b * ((a * i) - (z * c));
	t_4 = t_3 - (j * ((y * i) - (t * c)));
	tmp = 0.0;
	if (i <= -2.2e+152)
		tmp = (y * ((x * z) - (i * j))) + t_3;
	elseif (i <= -1.05e+91)
		tmp = t_1;
	elseif (i <= -7.7e+15)
		tmp = t_2 + t_3;
	elseif (i <= -7.6e-91)
		tmp = t_1;
	elseif (i <= -4.5e-171)
		tmp = t_4;
	elseif (i <= 1.15e-24)
		tmp = (t_2 - (x * ((t * a) - (y * z)))) - (b * (z * c));
	elseif (i <= 4.8e+131)
		tmp = t_4;
	else
		tmp = i * ((a * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.2e+152], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision], If[LessEqual[i, -1.05e+91], t$95$1, If[LessEqual[i, -7.7e+15], N[(t$95$2 + t$95$3), $MachinePrecision], If[LessEqual[i, -7.6e-91], t$95$1, If[LessEqual[i, -4.5e-171], t$95$4, If[LessEqual[i, 1.15e-24], N[(N[(t$95$2 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.8e+131], t$95$4, N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -2.1999999999999998e152

   1. Initial program 74.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 81.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 81.6%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 84.1%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 79.0%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 79.0%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 81.7%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 81.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 81.7%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 81.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 81.7%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 81.7%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   if -2.1999999999999998e152 < i < -1.05000000000000004e91 or -7.7e15 < i < -7.59999999999999957e-91

   1. Initial program 70.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 80.7%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   if -1.05000000000000004e91 < i < -7.7e15

   1. Initial program 64.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 64.9%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 64.9%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. *-commutative 64.9%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 64.9%

         \[\leadsto j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 64.9%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in y around 0 71.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 71.9%

         \[\leadsto c \cdot \left(j \cdot t\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

      2. *-commutative 71.9%

         \[\leadsto c \cdot \left(j \cdot t\right) - b \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right) \]

   8. Simplified 71.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right) - b \cdot \left(z \cdot c - i \cdot a\right)} \]

   if -7.59999999999999957e-91 < i < -4.5000000000000004e-171 or 1.1500000000000001e-24 < i < 4.7999999999999999e131

   1. Initial program 72.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 76.7%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 76.7%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. *-commutative 76.7%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 76.7%

         \[\leadsto j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 76.7%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   if -4.5000000000000004e-171 < i < 1.1500000000000001e-24

   1. Initial program 85.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 84.3%

      \[\leadsto \color{blue}{\left(c \cdot \left(j \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z\right)} \]

   if 4.7999999999999999e131 < i

   1. Initial program 52.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 78.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 78.0%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]

      2. *-commutative 78.0%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - a \cdot b\right)\right) \]

   5. Simplified 78.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - a \cdot b\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.2 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{+91}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq -7.7 \cdot 10^{+15}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq -7.6 \cdot 10^{-91}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq -4.5 \cdot 10^{-171}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{-24}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) - x \cdot \left(t \cdot a - y \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{+131}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 30.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-225}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-179}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-90}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-43}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+118} \lor \neg \left(z \leq 6 \cdot 10^{+188}\right) \land z \leq 2.3 \cdot 10^{+236}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -4.5e+42)
   (* x (* y z))
   (if (<= z 3.4e-225)
     (* (* i j) (- y))
     (if (<= z 1.15e-179)
       (* a (* b i))
       (if (<= z 6.6e-90)
         (* c (* t j))
         (if (<= z 1.6e-43)
           (* a (* t (- x)))
           (if (or (<= z 2.4e+118) (and (not (<= z 6e+188)) (<= z 2.3e+236)))
             (* b (* z (- c)))
             (* y (* x z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -4.5e+42) {
		tmp = x * (y * z);
	} else if (z <= 3.4e-225) {
		tmp = (i * j) * -y;
	} else if (z <= 1.15e-179) {
		tmp = a * (b * i);
	} else if (z <= 6.6e-90) {
		tmp = c * (t * j);
	} else if (z <= 1.6e-43) {
		tmp = a * (t * -x);
	} else if ((z <= 2.4e+118) || (!(z <= 6e+188) && (z <= 2.3e+236))) {
		tmp = b * (z * -c);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-4.5d+42)) then
        tmp = x * (y * z)
    else if (z <= 3.4d-225) then
        tmp = (i * j) * -y
    else if (z <= 1.15d-179) then
        tmp = a * (b * i)
    else if (z <= 6.6d-90) then
        tmp = c * (t * j)
    else if (z <= 1.6d-43) then
        tmp = a * (t * -x)
    else if ((z <= 2.4d+118) .or. (.not. (z <= 6d+188)) .and. (z <= 2.3d+236)) then
        tmp = b * (z * -c)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -4.5e+42) {
		tmp = x * (y * z);
	} else if (z <= 3.4e-225) {
		tmp = (i * j) * -y;
	} else if (z <= 1.15e-179) {
		tmp = a * (b * i);
	} else if (z <= 6.6e-90) {
		tmp = c * (t * j);
	} else if (z <= 1.6e-43) {
		tmp = a * (t * -x);
	} else if ((z <= 2.4e+118) || (!(z <= 6e+188) && (z <= 2.3e+236))) {
		tmp = b * (z * -c);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -4.5e+42:
		tmp = x * (y * z)
	elif z <= 3.4e-225:
		tmp = (i * j) * -y
	elif z <= 1.15e-179:
		tmp = a * (b * i)
	elif z <= 6.6e-90:
		tmp = c * (t * j)
	elif z <= 1.6e-43:
		tmp = a * (t * -x)
	elif (z <= 2.4e+118) or (not (z <= 6e+188) and (z <= 2.3e+236)):
		tmp = b * (z * -c)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -4.5e+42)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 3.4e-225)
		tmp = Float64(Float64(i * j) * Float64(-y));
	elseif (z <= 1.15e-179)
		tmp = Float64(a * Float64(b * i));
	elseif (z <= 6.6e-90)
		tmp = Float64(c * Float64(t * j));
	elseif (z <= 1.6e-43)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif ((z <= 2.4e+118) || (!(z <= 6e+188) && (z <= 2.3e+236)))
		tmp = Float64(b * Float64(z * Float64(-c)));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -4.5e+42)
		tmp = x * (y * z);
	elseif (z <= 3.4e-225)
		tmp = (i * j) * -y;
	elseif (z <= 1.15e-179)
		tmp = a * (b * i);
	elseif (z <= 6.6e-90)
		tmp = c * (t * j);
	elseif (z <= 1.6e-43)
		tmp = a * (t * -x);
	elseif ((z <= 2.4e+118) || (~((z <= 6e+188)) && (z <= 2.3e+236)))
		tmp = b * (z * -c);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -4.5e+42], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e-225], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[z, 1.15e-179], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e-90], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-43], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 2.4e+118], And[N[Not[LessEqual[z, 6e+188]], $MachinePrecision], LessEqual[z, 2.3e+236]]], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -4.50000000000000012e42

   1. Initial program 70.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 62.2%

      \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 62.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. associate-*r* 64.1%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right) \]

      3. associate-*r* 64.0%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right) \]

      4. distribute-rgt-out-- 66.0%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      5. +-commutative 66.0%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \]

      6. cancel-sign-sub-inv 66.0%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\left(c \cdot t + \left(-i\right) \cdot y\right)} \]

      7. *-commutative 66.0%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(\color{blue}{t \cdot c} + \left(-i\right) \cdot y\right) \]

      8. fma-udef 66.0%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)} \]

      9. fma-def 70.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, x \cdot y - b \cdot c, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right)} \]

      10. fma-neg 70.1%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(x, y, -b \cdot c\right)}, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      11. *-commutative 70.1%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, -\color{blue}{c \cdot b}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      12. distribute-rgt-neg-in 70.1%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, \color{blue}{c \cdot \left(-b\right)}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      13. distribute-lft-neg-out 70.1%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{-i \cdot y}\right)\right) \]

      14. distribute-rgt-neg-in 70.1%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{i \cdot \left(-y\right)}\right)\right) \]

   5. Simplified 70.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, i \cdot \left(-y\right)\right)\right)} \]

   6. Taylor expanded in x around inf 44.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if -4.50000000000000012e42 < z < 3.3999999999999999e-225

   1. Initial program 72.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 47.2%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   4. Taylor expanded in c around 0 37.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 40.9%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} \]

      2. associate-*r* 40.9%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} \]

      3. *-commutative 40.9%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg 40.9%

         \[\leadsto y \cdot \color{blue}{\left(-i \cdot j\right)} \]

      5. *-commutative 40.9%

         \[\leadsto y \cdot \left(-\color{blue}{j \cdot i}\right) \]

      6. distribute-rgt-neg-in 40.9%

         \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   6. Simplified 40.9%

      \[\leadsto \color{blue}{y \cdot \left(j \cdot \left(-i\right)\right)} \]

   if 3.3999999999999999e-225 < z < 1.14999999999999994e-179

   1. Initial program 86.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 51.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 51.8%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 51.8%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 51.8%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 51.8%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 51.8%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 51.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 51.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 51.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 51.8%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 51.8%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in a around inf 50.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 50.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

   8. Simplified 50.5%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   if 1.14999999999999994e-179 < z < 6.6e-90

   1. Initial program 86.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 50.6%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.6%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 50.6%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 50.6%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 50.6%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 50.6%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   5. Simplified 50.6%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]

   6. Taylor expanded in j around inf 43.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if 6.6e-90 < z < 1.59999999999999992e-43

   1. Initial program 88.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 45.9%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 45.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 45.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 45.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 45.9%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 45.9%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   5. Simplified 45.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]

   6. Taylor expanded in j around 0 45.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 45.8%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} \]

      2. neg-mul-1 45.8%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) \]

      3. *-commutative 45.8%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(x \cdot t\right)} \]

   8. Simplified 45.8%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot t\right)} \]

   if 1.59999999999999992e-43 < z < 2.4e118 or 6.0000000000000001e188 < z < 2.3e236

   1. Initial program 75.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 68.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 68.9%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 71.4%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 69.2%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 69.2%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 75.8%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 75.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 75.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 75.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 75.8%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 75.8%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in c around inf 54.8%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 54.8%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. neg-mul-1 54.8%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right) \]

      3. *-commutative 54.8%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(z \cdot c\right)} \]

   8. Simplified 54.8%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(z \cdot c\right)} \]

   if 2.4e118 < z < 6.0000000000000001e188 or 2.3e236 < z

   1. Initial program 52.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 49.3%

      \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 49.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. associate-*r* 59.6%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right) \]

      3. associate-*r* 70.2%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right) \]

      4. distribute-rgt-out-- 70.2%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      5. +-commutative 70.2%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \]

      6. cancel-sign-sub-inv 70.2%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\left(c \cdot t + \left(-i\right) \cdot y\right)} \]

      7. *-commutative 70.2%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(\color{blue}{t \cdot c} + \left(-i\right) \cdot y\right) \]

      8. fma-udef 70.2%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)} \]

      9. fma-def 70.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, x \cdot y - b \cdot c, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right)} \]

      10. fma-neg 70.2%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(x, y, -b \cdot c\right)}, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      11. *-commutative 70.2%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, -\color{blue}{c \cdot b}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      12. distribute-rgt-neg-in 70.2%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, \color{blue}{c \cdot \left(-b\right)}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      13. distribute-lft-neg-out 70.2%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{-i \cdot y}\right)\right) \]

      14. distribute-rgt-neg-in 70.2%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{i \cdot \left(-y\right)}\right)\right) \]

   5. Simplified 70.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, i \cdot \left(-y\right)\right)\right)} \]

   6. Taylor expanded in x around inf 50.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 50.5%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. associate-*l* 67.5%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   8. Simplified 67.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-225}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-179}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-90}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-43}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+118} \lor \neg \left(z \leq 6 \cdot 10^{+188}\right) \land z \leq 2.3 \cdot 10^{+236}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -3.35 \cdot 10^{+137}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-5}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y (- (* x z) (* i j))) (* z (* b c))))
        (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -3.35e+137)
     t_2
     (if (<= t -3.3e+25)
       t_1
       (if (<= t -3.7e-39)
         (- (* x (* y z)) (* j (- (* y i) (* t c))))
         (if (<= t 2.6e-72)
           t_1
           (if (<= t 2.7e-5)
             (+ (* c (* t j)) (* b (- (* a i) (* z c))))
             (if (<= t 5.3e+104) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) - (z * (b * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -3.35e+137) {
		tmp = t_2;
	} else if (t <= -3.3e+25) {
		tmp = t_1;
	} else if (t <= -3.7e-39) {
		tmp = (x * (y * z)) - (j * ((y * i) - (t * c)));
	} else if (t <= 2.6e-72) {
		tmp = t_1;
	} else if (t <= 2.7e-5) {
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)));
	} else if (t <= 5.3e+104) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * ((x * z) - (i * j))) - (z * (b * c))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-3.35d+137)) then
        tmp = t_2
    else if (t <= (-3.3d+25)) then
        tmp = t_1
    else if (t <= (-3.7d-39)) then
        tmp = (x * (y * z)) - (j * ((y * i) - (t * c)))
    else if (t <= 2.6d-72) then
        tmp = t_1
    else if (t <= 2.7d-5) then
        tmp = (c * (t * j)) + (b * ((a * i) - (z * c)))
    else if (t <= 5.3d+104) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) - (z * (b * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -3.35e+137) {
		tmp = t_2;
	} else if (t <= -3.3e+25) {
		tmp = t_1;
	} else if (t <= -3.7e-39) {
		tmp = (x * (y * z)) - (j * ((y * i) - (t * c)));
	} else if (t <= 2.6e-72) {
		tmp = t_1;
	} else if (t <= 2.7e-5) {
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)));
	} else if (t <= 5.3e+104) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * ((x * z) - (i * j))) - (z * (b * c))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -3.35e+137:
		tmp = t_2
	elif t <= -3.3e+25:
		tmp = t_1
	elif t <= -3.7e-39:
		tmp = (x * (y * z)) - (j * ((y * i) - (t * c)))
	elif t <= 2.6e-72:
		tmp = t_1
	elif t <= 2.7e-5:
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)))
	elif t <= 5.3e+104:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(z * Float64(b * c)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -3.35e+137)
		tmp = t_2;
	elseif (t <= -3.3e+25)
		tmp = t_1;
	elseif (t <= -3.7e-39)
		tmp = Float64(Float64(x * Float64(y * z)) - Float64(j * Float64(Float64(y * i) - Float64(t * c))));
	elseif (t <= 2.6e-72)
		tmp = t_1;
	elseif (t <= 2.7e-5)
		tmp = Float64(Float64(c * Float64(t * j)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (t <= 5.3e+104)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * ((x * z) - (i * j))) - (z * (b * c));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -3.35e+137)
		tmp = t_2;
	elseif (t <= -3.3e+25)
		tmp = t_1;
	elseif (t <= -3.7e-39)
		tmp = (x * (y * z)) - (j * ((y * i) - (t * c)));
	elseif (t <= 2.6e-72)
		tmp = t_1;
	elseif (t <= 2.7e-5)
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)));
	elseif (t <= 5.3e+104)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.35e+137], t$95$2, If[LessEqual[t, -3.3e+25], t$95$1, If[LessEqual[t, -3.7e-39], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e-72], t$95$1, If[LessEqual[t, 2.7e-5], N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.3e+104], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.3499999999999999e137 or 5.2999999999999999e104 < t

   1. Initial program 59.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 72.2%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 72.2%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 72.2%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 72.2%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 72.2%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 72.2%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   5. Simplified 72.2%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]

   if -3.3499999999999999e137 < t < -3.3000000000000001e25 or -3.70000000000000015e-39 < t < 2.59999999999999996e-72 or 2.6999999999999999e-5 < t < 5.2999999999999999e104

   1. Initial program 77.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 72.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 72.2%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 72.9%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 72.9%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 72.9%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 75.6%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 75.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 75.6%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 75.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 75.6%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 75.6%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in z around inf 69.5%

      \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - \color{blue}{b \cdot \left(c \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 69.5%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \color{blue}{\left(z \cdot c\right)} \]

      2. *-commutative 69.5%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - \color{blue}{\left(z \cdot c\right) \cdot b} \]

      3. associate-*l* 70.3%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - \color{blue}{z \cdot \left(c \cdot b\right)} \]

      4. *-commutative 70.3%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \color{blue}{\left(b \cdot c\right)} \]

   8. Simplified 70.3%

      \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - \color{blue}{z \cdot \left(b \cdot c\right)} \]

   if -3.3000000000000001e25 < t < -3.70000000000000015e-39

   1. Initial program 86.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 75.0%

      \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 75.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. associate-*r* 75.0%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right) \]

      3. associate-*r* 68.3%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right) \]

      4. distribute-rgt-out-- 68.3%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      5. +-commutative 68.3%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \]

      6. cancel-sign-sub-inv 68.3%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\left(c \cdot t + \left(-i\right) \cdot y\right)} \]

      7. *-commutative 68.3%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(\color{blue}{t \cdot c} + \left(-i\right) \cdot y\right) \]

      8. fma-udef 68.3%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)} \]

      9. fma-def 68.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, x \cdot y - b \cdot c, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right)} \]

      10. fma-neg 68.3%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(x, y, -b \cdot c\right)}, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      11. *-commutative 68.3%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, -\color{blue}{c \cdot b}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      12. distribute-rgt-neg-in 68.3%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, \color{blue}{c \cdot \left(-b\right)}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      13. distribute-lft-neg-out 68.3%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{-i \cdot y}\right)\right) \]

      14. distribute-rgt-neg-in 68.3%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{i \cdot \left(-y\right)}\right)\right) \]

   5. Simplified 68.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, i \cdot \left(-y\right)\right)\right)} \]

   6. Taylor expanded in b around 0 68.8%

      \[\leadsto \color{blue}{j \cdot \left(-1 \cdot \left(i \cdot y\right) + c \cdot t\right) + x \cdot \left(y \cdot z\right)} \]

   if 2.59999999999999996e-72 < t < 2.6999999999999999e-5

   1. Initial program 74.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.1%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 81.1%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. *-commutative 81.1%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 81.1%

         \[\leadsto j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 81.1%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in y around 0 75.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 75.5%

         \[\leadsto c \cdot \left(j \cdot t\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

      2. *-commutative 75.5%

         \[\leadsto c \cdot \left(j \cdot t\right) - b \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right) \]

   8. Simplified 75.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right) - b \cdot \left(z \cdot c - i \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.35 \cdot 10^{+137}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+25}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-72}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-5}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+104}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.35 \cdot 10^{+41}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.08 \cdot 10^{-160}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-102}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+14}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+63}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* t (- (* c j) (* x a))))
        (t_3 (* b (- (* a i) (* z c)))))
   (if (<= b -3.35e+41)
     t_3
     (if (<= b -2.7e-100)
       t_1
       (if (<= b -1.08e-160)
         (* y (* x z))
         (if (<= b -3e-174)
           t_1
           (if (<= b 4.8e-102)
             t_2
             (if (<= b 1.95e+14)
               (* c (- (* t j) (* z b)))
               (if (<= b 6.2e+63) t_2 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.35e+41) {
		tmp = t_3;
	} else if (b <= -2.7e-100) {
		tmp = t_1;
	} else if (b <= -1.08e-160) {
		tmp = y * (x * z);
	} else if (b <= -3e-174) {
		tmp = t_1;
	} else if (b <= 4.8e-102) {
		tmp = t_2;
	} else if (b <= 1.95e+14) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 6.2e+63) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = t * ((c * j) - (x * a))
    t_3 = b * ((a * i) - (z * c))
    if (b <= (-3.35d+41)) then
        tmp = t_3
    else if (b <= (-2.7d-100)) then
        tmp = t_1
    else if (b <= (-1.08d-160)) then
        tmp = y * (x * z)
    else if (b <= (-3d-174)) then
        tmp = t_1
    else if (b <= 4.8d-102) then
        tmp = t_2
    else if (b <= 1.95d+14) then
        tmp = c * ((t * j) - (z * b))
    else if (b <= 6.2d+63) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = t * ((c * j) - (x * a));
	double t_3 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.35e+41) {
		tmp = t_3;
	} else if (b <= -2.7e-100) {
		tmp = t_1;
	} else if (b <= -1.08e-160) {
		tmp = y * (x * z);
	} else if (b <= -3e-174) {
		tmp = t_1;
	} else if (b <= 4.8e-102) {
		tmp = t_2;
	} else if (b <= 1.95e+14) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 6.2e+63) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = t * ((c * j) - (x * a))
	t_3 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -3.35e+41:
		tmp = t_3
	elif b <= -2.7e-100:
		tmp = t_1
	elif b <= -1.08e-160:
		tmp = y * (x * z)
	elif b <= -3e-174:
		tmp = t_1
	elif b <= 4.8e-102:
		tmp = t_2
	elif b <= 1.95e+14:
		tmp = c * ((t * j) - (z * b))
	elif b <= 6.2e+63:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_3 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.35e+41)
		tmp = t_3;
	elseif (b <= -2.7e-100)
		tmp = t_1;
	elseif (b <= -1.08e-160)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= -3e-174)
		tmp = t_1;
	elseif (b <= 4.8e-102)
		tmp = t_2;
	elseif (b <= 1.95e+14)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (b <= 6.2e+63)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = t * ((c * j) - (x * a));
	t_3 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.35e+41)
		tmp = t_3;
	elseif (b <= -2.7e-100)
		tmp = t_1;
	elseif (b <= -1.08e-160)
		tmp = y * (x * z);
	elseif (b <= -3e-174)
		tmp = t_1;
	elseif (b <= 4.8e-102)
		tmp = t_2;
	elseif (b <= 1.95e+14)
		tmp = c * ((t * j) - (z * b));
	elseif (b <= 6.2e+63)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.35e+41], t$95$3, If[LessEqual[b, -2.7e-100], t$95$1, If[LessEqual[b, -1.08e-160], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3e-174], t$95$1, If[LessEqual[b, 4.8e-102], t$95$2, If[LessEqual[b, 1.95e+14], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.2e+63], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.3499999999999998e41 or 6.2000000000000001e63 < b

   1. Initial program 74.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 67.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 67.4%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 67.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   if -3.3499999999999998e41 < b < -2.70000000000000016e-100 or -1.08e-160 < b < -3.00000000000000021e-174

   1. Initial program 85.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 52.0%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   if -2.70000000000000016e-100 < b < -1.08e-160

   1. Initial program 47.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 54.9%

      \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 54.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. associate-*r* 69.1%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right) \]

      3. associate-*r* 69.1%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right) \]

      4. distribute-rgt-out-- 69.1%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      5. +-commutative 69.1%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \]

      6. cancel-sign-sub-inv 69.1%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\left(c \cdot t + \left(-i\right) \cdot y\right)} \]

      7. *-commutative 69.1%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(\color{blue}{t \cdot c} + \left(-i\right) \cdot y\right) \]

      8. fma-udef 69.1%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)} \]

      9. fma-def 69.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, x \cdot y - b \cdot c, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right)} \]

      10. fma-neg 69.1%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(x, y, -b \cdot c\right)}, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      11. *-commutative 69.1%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, -\color{blue}{c \cdot b}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      12. distribute-rgt-neg-in 69.1%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, \color{blue}{c \cdot \left(-b\right)}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      13. distribute-lft-neg-out 69.1%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{-i \cdot y}\right)\right) \]

      14. distribute-rgt-neg-in 69.1%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{i \cdot \left(-y\right)}\right)\right) \]

   5. Simplified 69.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, i \cdot \left(-y\right)\right)\right)} \]

   6. Taylor expanded in x around inf 56.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 56.3%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. associate-*l* 63.4%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   8. Simplified 63.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -3.00000000000000021e-174 < b < 4.8e-102 or 1.95e14 < b < 6.2000000000000001e63

   1. Initial program 65.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 48.3%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.3%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 48.3%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 48.3%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 48.3%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 48.3%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   5. Simplified 48.3%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]

   if 4.8e-102 < b < 1.95e14

   1. Initial program 82.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 53.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 53.2%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 53.2%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   5. Simplified 53.2%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.35 \cdot 10^{+41}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-100}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -1.08 \cdot 10^{-160}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-174}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-102}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+14}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{if}\;c \leq -8 \cdot 10^{+185}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) - x \cdot \left(t \cdot a\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{+21}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq -9 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 10^{-73}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y (- (* x z) (* i j))) (* z (* b c)))))
   (if (<= c -8e+185)
     (- (- (* c (* t j)) (* x (* t a))) (* b (* z c)))
     (if (<= c -6.8e+56)
       t_1
       (if (<= c -3.1e+21)
         (* a (- (* b i) (* x t)))
         (if (<= c -9e-91)
           t_1
           (if (<= c 1e-73)
             (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a))))
             (- (* b (- (* a i) (* z c))) (* j (- (* y i) (* t c)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) - (z * (b * c));
	double tmp;
	if (c <= -8e+185) {
		tmp = ((c * (t * j)) - (x * (t * a))) - (b * (z * c));
	} else if (c <= -6.8e+56) {
		tmp = t_1;
	} else if (c <= -3.1e+21) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= -9e-91) {
		tmp = t_1;
	} else if (c <= 1e-73) {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (b * ((a * i) - (z * c))) - (j * ((y * i) - (t * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * ((x * z) - (i * j))) - (z * (b * c))
    if (c <= (-8d+185)) then
        tmp = ((c * (t * j)) - (x * (t * a))) - (b * (z * c))
    else if (c <= (-6.8d+56)) then
        tmp = t_1
    else if (c <= (-3.1d+21)) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= (-9d-91)) then
        tmp = t_1
    else if (c <= 1d-73) then
        tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else
        tmp = (b * ((a * i) - (z * c))) - (j * ((y * i) - (t * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) - (z * (b * c));
	double tmp;
	if (c <= -8e+185) {
		tmp = ((c * (t * j)) - (x * (t * a))) - (b * (z * c));
	} else if (c <= -6.8e+56) {
		tmp = t_1;
	} else if (c <= -3.1e+21) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= -9e-91) {
		tmp = t_1;
	} else if (c <= 1e-73) {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (b * ((a * i) - (z * c))) - (j * ((y * i) - (t * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * ((x * z) - (i * j))) - (z * (b * c))
	tmp = 0
	if c <= -8e+185:
		tmp = ((c * (t * j)) - (x * (t * a))) - (b * (z * c))
	elif c <= -6.8e+56:
		tmp = t_1
	elif c <= -3.1e+21:
		tmp = a * ((b * i) - (x * t))
	elif c <= -9e-91:
		tmp = t_1
	elif c <= 1e-73:
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	else:
		tmp = (b * ((a * i) - (z * c))) - (j * ((y * i) - (t * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(z * Float64(b * c)))
	tmp = 0.0
	if (c <= -8e+185)
		tmp = Float64(Float64(Float64(c * Float64(t * j)) - Float64(x * Float64(t * a))) - Float64(b * Float64(z * c)));
	elseif (c <= -6.8e+56)
		tmp = t_1;
	elseif (c <= -3.1e+21)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= -9e-91)
		tmp = t_1;
	elseif (c <= 1e-73)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) - Float64(j * Float64(Float64(y * i) - Float64(t * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * ((x * z) - (i * j))) - (z * (b * c));
	tmp = 0.0;
	if (c <= -8e+185)
		tmp = ((c * (t * j)) - (x * (t * a))) - (b * (z * c));
	elseif (c <= -6.8e+56)
		tmp = t_1;
	elseif (c <= -3.1e+21)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= -9e-91)
		tmp = t_1;
	elseif (c <= 1e-73)
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	else
		tmp = (b * ((a * i) - (z * c))) - (j * ((y * i) - (t * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8e+185], N[(N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] - N[(x * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -6.8e+56], t$95$1, If[LessEqual[c, -3.1e+21], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -9e-91], t$95$1, If[LessEqual[c, 1e-73], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -7.9999999999999998e185

   1. Initial program 75.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 87.4%

      \[\leadsto \color{blue}{\left(c \cdot \left(j \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z\right)} \]

   4. Taylor expanded in y around 0 83.5%

      \[\leadsto \left(c \cdot \left(j \cdot t\right) + \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 83.5%

         \[\leadsto \left(c \cdot \left(j \cdot t\right) + \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)}\right) - b \cdot \left(c \cdot z\right) \]

      2. associate-*r* 87.4%

         \[\leadsto \left(c \cdot \left(j \cdot t\right) + \left(-\color{blue}{\left(a \cdot t\right) \cdot x}\right)\right) - b \cdot \left(c \cdot z\right) \]

      3. *-commutative 87.4%

         \[\leadsto \left(c \cdot \left(j \cdot t\right) + \left(-\color{blue}{x \cdot \left(a \cdot t\right)}\right)\right) - b \cdot \left(c \cdot z\right) \]

   6. Simplified 87.4%

      \[\leadsto \left(c \cdot \left(j \cdot t\right) + \color{blue}{\left(-x \cdot \left(a \cdot t\right)\right)}\right) - b \cdot \left(c \cdot z\right) \]

   if -7.9999999999999998e185 < c < -6.80000000000000002e56 or -3.1e21 < c < -8.99999999999999952e-91

   1. Initial program 67.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 70.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 70.8%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 75.0%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 77.2%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 77.2%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 79.5%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 79.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 79.5%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 79.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 79.5%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 79.5%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in z around inf 77.4%

      \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - \color{blue}{b \cdot \left(c \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 77.4%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \color{blue}{\left(z \cdot c\right)} \]

      2. *-commutative 77.4%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - \color{blue}{\left(z \cdot c\right) \cdot b} \]

      3. associate-*l* 79.6%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - \color{blue}{z \cdot \left(c \cdot b\right)} \]

      4. *-commutative 79.6%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \color{blue}{\left(b \cdot c\right)} \]

   8. Simplified 79.6%

      \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - \color{blue}{z \cdot \left(b \cdot c\right)} \]

   if -6.80000000000000002e56 < c < -3.1e21

   1. Initial program 75.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around -inf 75.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)} \]

   if -8.99999999999999952e-91 < c < 9.99999999999999997e-74

   1. Initial program 73.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 68.5%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   if 9.99999999999999997e-74 < c

   1. Initial program 73.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 72.2%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 72.2%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. *-commutative 72.2%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 72.2%

         \[\leadsto j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 72.2%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8 \cdot 10^{+185}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) - x \cdot \left(t \cdot a\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{+56}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{+21}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq -9 \cdot 10^{-91}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;c \leq 10^{-73}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 41.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{+50}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-117}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-72}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+190}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+202}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= y -5e+50)
     (* i (* y (- j)))
     (if (<= y 1.32e-117)
       (* b (- (* a i) (* z c)))
       (if (<= y 1.75e-72)
         (* a (* t (- x)))
         (if (<= y 4.2e+75)
           t_1
           (if (<= y 1.8e+190)
             (* x (* y z))
             (if (<= y 4.2e+202) t_1 (* (* i j) (- y))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (y <= -5e+50) {
		tmp = i * (y * -j);
	} else if (y <= 1.32e-117) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= 1.75e-72) {
		tmp = a * (t * -x);
	} else if (y <= 4.2e+75) {
		tmp = t_1;
	} else if (y <= 1.8e+190) {
		tmp = x * (y * z);
	} else if (y <= 4.2e+202) {
		tmp = t_1;
	} else {
		tmp = (i * j) * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    if (y <= (-5d+50)) then
        tmp = i * (y * -j)
    else if (y <= 1.32d-117) then
        tmp = b * ((a * i) - (z * c))
    else if (y <= 1.75d-72) then
        tmp = a * (t * -x)
    else if (y <= 4.2d+75) then
        tmp = t_1
    else if (y <= 1.8d+190) then
        tmp = x * (y * z)
    else if (y <= 4.2d+202) then
        tmp = t_1
    else
        tmp = (i * j) * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (y <= -5e+50) {
		tmp = i * (y * -j);
	} else if (y <= 1.32e-117) {
		tmp = b * ((a * i) - (z * c));
	} else if (y <= 1.75e-72) {
		tmp = a * (t * -x);
	} else if (y <= 4.2e+75) {
		tmp = t_1;
	} else if (y <= 1.8e+190) {
		tmp = x * (y * z);
	} else if (y <= 4.2e+202) {
		tmp = t_1;
	} else {
		tmp = (i * j) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if y <= -5e+50:
		tmp = i * (y * -j)
	elif y <= 1.32e-117:
		tmp = b * ((a * i) - (z * c))
	elif y <= 1.75e-72:
		tmp = a * (t * -x)
	elif y <= 4.2e+75:
		tmp = t_1
	elif y <= 1.8e+190:
		tmp = x * (y * z)
	elif y <= 4.2e+202:
		tmp = t_1
	else:
		tmp = (i * j) * -y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (y <= -5e+50)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (y <= 1.32e-117)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (y <= 1.75e-72)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (y <= 4.2e+75)
		tmp = t_1;
	elseif (y <= 1.8e+190)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= 4.2e+202)
		tmp = t_1;
	else
		tmp = Float64(Float64(i * j) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (y <= -5e+50)
		tmp = i * (y * -j);
	elseif (y <= 1.32e-117)
		tmp = b * ((a * i) - (z * c));
	elseif (y <= 1.75e-72)
		tmp = a * (t * -x);
	elseif (y <= 4.2e+75)
		tmp = t_1;
	elseif (y <= 1.8e+190)
		tmp = x * (y * z);
	elseif (y <= 4.2e+202)
		tmp = t_1;
	else
		tmp = (i * j) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+50], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.32e-117], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e-72], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+75], t$95$1, If[LessEqual[y, 1.8e+190], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+202], t$95$1, N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -5e50

   1. Initial program 63.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 43.7%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   4. Taylor expanded in c around 0 42.4%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 42.4%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. neg-mul-1 42.4%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

      3. *-commutative 42.4%

         \[\leadsto \left(-i\right) \cdot \color{blue}{\left(y \cdot j\right)} \]

   6. Simplified 42.4%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   if -5e50 < y < 1.32e-117

   1. Initial program 79.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 52.9%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 52.9%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 52.9%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   if 1.32e-117 < y < 1.75e-72

   1. Initial program 74.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 75.4%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 75.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 75.4%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 75.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 75.4%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 75.4%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   5. Simplified 75.4%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]

   6. Taylor expanded in j around 0 75.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 75.3%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} \]

      2. neg-mul-1 75.3%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) \]

      3. *-commutative 75.3%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(x \cdot t\right)} \]

   8. Simplified 75.3%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot t\right)} \]

   if 1.75e-72 < y < 4.19999999999999997e75 or 1.79999999999999989e190 < y < 4.2e202

   1. Initial program 82.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 57.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 57.7%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 57.7%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   5. Simplified 57.7%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   if 4.19999999999999997e75 < y < 1.79999999999999989e190

   1. Initial program 65.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 63.2%

      \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 63.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. associate-*r* 65.2%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right) \]

      3. associate-*r* 61.7%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right) \]

      4. distribute-rgt-out-- 65.2%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      5. +-commutative 65.2%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \]

      6. cancel-sign-sub-inv 65.2%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\left(c \cdot t + \left(-i\right) \cdot y\right)} \]

      7. *-commutative 65.2%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(\color{blue}{t \cdot c} + \left(-i\right) \cdot y\right) \]

      8. fma-udef 65.2%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)} \]

      9. fma-def 65.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, x \cdot y - b \cdot c, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right)} \]

      10. fma-neg 65.2%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(x, y, -b \cdot c\right)}, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      11. *-commutative 65.2%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, -\color{blue}{c \cdot b}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      12. distribute-rgt-neg-in 65.2%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, \color{blue}{c \cdot \left(-b\right)}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      13. distribute-lft-neg-out 65.2%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{-i \cdot y}\right)\right) \]

      14. distribute-rgt-neg-in 65.2%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{i \cdot \left(-y\right)}\right)\right) \]

   5. Simplified 65.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, i \cdot \left(-y\right)\right)\right)} \]

   6. Taylor expanded in x around inf 42.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 4.2e202 < y

   1. Initial program 64.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 80.5%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   4. Taylor expanded in c around 0 69.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 76.7%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} \]

      2. associate-*r* 76.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} \]

      3. *-commutative 76.7%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg 76.7%

         \[\leadsto y \cdot \color{blue}{\left(-i \cdot j\right)} \]

      5. *-commutative 76.7%

         \[\leadsto y \cdot \left(-\color{blue}{j \cdot i}\right) \]

      6. distribute-rgt-neg-in 76.7%

         \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   6. Simplified 76.7%

      \[\leadsto \color{blue}{y \cdot \left(j \cdot \left(-i\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+50}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-117}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-72}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+75}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+190}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+202}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.3 \cdot 10^{+49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{-100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8.6 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-250}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -4.3e+49)
     t_2
     (if (<= b -4.4e-100)
       t_1
       (if (<= b -8.6e-159)
         (* y (* x z))
         (if (<= b -3.5e-176)
           t_1
           (if (<= b -1.55e-250)
             (* t (* x (- a)))
             (if (<= b 4e+60) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4.3e+49) {
		tmp = t_2;
	} else if (b <= -4.4e-100) {
		tmp = t_1;
	} else if (b <= -8.6e-159) {
		tmp = y * (x * z);
	} else if (b <= -3.5e-176) {
		tmp = t_1;
	} else if (b <= -1.55e-250) {
		tmp = t * (x * -a);
	} else if (b <= 4e+60) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-4.3d+49)) then
        tmp = t_2
    else if (b <= (-4.4d-100)) then
        tmp = t_1
    else if (b <= (-8.6d-159)) then
        tmp = y * (x * z)
    else if (b <= (-3.5d-176)) then
        tmp = t_1
    else if (b <= (-1.55d-250)) then
        tmp = t * (x * -a)
    else if (b <= 4d+60) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4.3e+49) {
		tmp = t_2;
	} else if (b <= -4.4e-100) {
		tmp = t_1;
	} else if (b <= -8.6e-159) {
		tmp = y * (x * z);
	} else if (b <= -3.5e-176) {
		tmp = t_1;
	} else if (b <= -1.55e-250) {
		tmp = t * (x * -a);
	} else if (b <= 4e+60) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -4.3e+49:
		tmp = t_2
	elif b <= -4.4e-100:
		tmp = t_1
	elif b <= -8.6e-159:
		tmp = y * (x * z)
	elif b <= -3.5e-176:
		tmp = t_1
	elif b <= -1.55e-250:
		tmp = t * (x * -a)
	elif b <= 4e+60:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4.3e+49)
		tmp = t_2;
	elseif (b <= -4.4e-100)
		tmp = t_1;
	elseif (b <= -8.6e-159)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= -3.5e-176)
		tmp = t_1;
	elseif (b <= -1.55e-250)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (b <= 4e+60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -4.3e+49)
		tmp = t_2;
	elseif (b <= -4.4e-100)
		tmp = t_1;
	elseif (b <= -8.6e-159)
		tmp = y * (x * z);
	elseif (b <= -3.5e-176)
		tmp = t_1;
	elseif (b <= -1.55e-250)
		tmp = t * (x * -a);
	elseif (b <= 4e+60)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.3e+49], t$95$2, If[LessEqual[b, -4.4e-100], t$95$1, If[LessEqual[b, -8.6e-159], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.5e-176], t$95$1, If[LessEqual[b, -1.55e-250], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e+60], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.2999999999999999e49 or 3.9999999999999998e60 < b

   1. Initial program 74.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 66.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 66.8%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 66.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   if -4.2999999999999999e49 < b < -4.39999999999999978e-100 or -8.6e-159 < b < -3.5e-176 or -1.5500000000000001e-250 < b < 3.9999999999999998e60

   1. Initial program 73.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 45.9%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   if -4.39999999999999978e-100 < b < -8.6e-159

   1. Initial program 47.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 54.9%

      \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 54.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. associate-*r* 69.1%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right) \]

      3. associate-*r* 69.1%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right) \]

      4. distribute-rgt-out-- 69.1%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      5. +-commutative 69.1%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \]

      6. cancel-sign-sub-inv 69.1%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\left(c \cdot t + \left(-i\right) \cdot y\right)} \]

      7. *-commutative 69.1%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(\color{blue}{t \cdot c} + \left(-i\right) \cdot y\right) \]

      8. fma-udef 69.1%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)} \]

      9. fma-def 69.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, x \cdot y - b \cdot c, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right)} \]

      10. fma-neg 69.1%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(x, y, -b \cdot c\right)}, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      11. *-commutative 69.1%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, -\color{blue}{c \cdot b}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      12. distribute-rgt-neg-in 69.1%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, \color{blue}{c \cdot \left(-b\right)}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      13. distribute-lft-neg-out 69.1%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{-i \cdot y}\right)\right) \]

      14. distribute-rgt-neg-in 69.1%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{i \cdot \left(-y\right)}\right)\right) \]

   5. Simplified 69.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, i \cdot \left(-y\right)\right)\right)} \]

   6. Taylor expanded in x around inf 56.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 56.3%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. associate-*l* 63.4%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   8. Simplified 63.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -3.5e-176 < b < -1.5500000000000001e-250

   1. Initial program 71.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 58.7%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 58.7%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 58.7%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 58.7%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 58.7%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 58.7%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   5. Simplified 58.7%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]

   6. Taylor expanded in j around 0 41.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 41.3%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} \]

      2. neg-mul-1 41.3%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) \]

      3. *-commutative 41.3%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(x \cdot t\right)} \]

      4. associate-*r* 45.2%

         \[\leadsto \color{blue}{\left(\left(-a\right) \cdot x\right) \cdot t} \]

      5. distribute-lft-neg-in 45.2%

         \[\leadsto \color{blue}{\left(-a \cdot x\right)} \cdot t \]

      6. *-commutative 45.2%

         \[\leadsto \left(-\color{blue}{x \cdot a}\right) \cdot t \]

      7. distribute-rgt-neg-in 45.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(-a\right)\right)} \cdot t \]

   8. Simplified 45.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(-a\right)\right) \cdot t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.3 \cdot 10^{+49}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{-100}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -8.6 \cdot 10^{-159}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-176}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-250}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+60}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+50}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-24}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-123}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+70}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* y (- (* x z) (* i j)))))
   (if (<= y -1.7e+50)
     t_3
     (if (<= y -2.1e-24)
       t_2
       (if (<= y -2.5e-91)
         t_1
         (if (<= y 7.6e-123)
           t_2
           (if (<= y 2.15e-68)
             t_1
             (if (<= y 3.6e+70) (* c (- (* t j) (* z b))) t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.7e+50) {
		tmp = t_3;
	} else if (y <= -2.1e-24) {
		tmp = t_2;
	} else if (y <= -2.5e-91) {
		tmp = t_1;
	} else if (y <= 7.6e-123) {
		tmp = t_2;
	} else if (y <= 2.15e-68) {
		tmp = t_1;
	} else if (y <= 3.6e+70) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    t_2 = b * ((a * i) - (z * c))
    t_3 = y * ((x * z) - (i * j))
    if (y <= (-1.7d+50)) then
        tmp = t_3
    else if (y <= (-2.1d-24)) then
        tmp = t_2
    else if (y <= (-2.5d-91)) then
        tmp = t_1
    else if (y <= 7.6d-123) then
        tmp = t_2
    else if (y <= 2.15d-68) then
        tmp = t_1
    else if (y <= 3.6d+70) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.7e+50) {
		tmp = t_3;
	} else if (y <= -2.1e-24) {
		tmp = t_2;
	} else if (y <= -2.5e-91) {
		tmp = t_1;
	} else if (y <= 7.6e-123) {
		tmp = t_2;
	} else if (y <= 2.15e-68) {
		tmp = t_1;
	} else if (y <= 3.6e+70) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = b * ((a * i) - (z * c))
	t_3 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.7e+50:
		tmp = t_3
	elif y <= -2.1e-24:
		tmp = t_2
	elif y <= -2.5e-91:
		tmp = t_1
	elif y <= 7.6e-123:
		tmp = t_2
	elif y <= 2.15e-68:
		tmp = t_1
	elif y <= 3.6e+70:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.7e+50)
		tmp = t_3;
	elseif (y <= -2.1e-24)
		tmp = t_2;
	elseif (y <= -2.5e-91)
		tmp = t_1;
	elseif (y <= 7.6e-123)
		tmp = t_2;
	elseif (y <= 2.15e-68)
		tmp = t_1;
	elseif (y <= 3.6e+70)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = b * ((a * i) - (z * c));
	t_3 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.7e+50)
		tmp = t_3;
	elseif (y <= -2.1e-24)
		tmp = t_2;
	elseif (y <= -2.5e-91)
		tmp = t_1;
	elseif (y <= 7.6e-123)
		tmp = t_2;
	elseif (y <= 2.15e-68)
		tmp = t_1;
	elseif (y <= 3.6e+70)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+50], t$95$3, If[LessEqual[y, -2.1e-24], t$95$2, If[LessEqual[y, -2.5e-91], t$95$1, If[LessEqual[y, 7.6e-123], t$95$2, If[LessEqual[y, 2.15e-68], t$95$1, If[LessEqual[y, 3.6e+70], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6999999999999999e50 or 3.6e70 < y

   1. Initial program 64.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 70.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 70.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 70.7%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 70.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

   5. Simplified 70.7%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right)} \]

   if -1.6999999999999999e50 < y < -2.0999999999999999e-24 or -2.49999999999999999e-91 < y < 7.59999999999999991e-123

   1. Initial program 79.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 60.5%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 60.5%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 60.5%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   if -2.0999999999999999e-24 < y < -2.49999999999999999e-91 or 7.59999999999999991e-123 < y < 2.15000000000000005e-68

   1. Initial program 75.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 61.7%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 61.7%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 61.7%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 61.7%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 61.7%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 61.7%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   5. Simplified 61.7%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]

   if 2.15000000000000005e-68 < y < 3.6e70

   1. Initial program 82.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 57.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 57.0%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 57.0%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   5. Simplified 57.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-24}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-91}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-123}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-68}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+70}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{+138}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-39}:\\ \;\;\;\;t\_1 - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;t \leq -1.52 \cdot 10^{-83}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -1.45e+138)
     t_2
     (if (<= t -3.8e-39)
       (- t_1 (* j (- (* y i) (* t c))))
       (if (<= t -1.52e-83)
         (- (+ (* c (* t j)) (* x (* y z))) (* b (* z c)))
         (if (<= t 3.9e+102) (+ (* y (- (* x z) (* i j))) t_1) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1.45e+138) {
		tmp = t_2;
	} else if (t <= -3.8e-39) {
		tmp = t_1 - (j * ((y * i) - (t * c)));
	} else if (t <= -1.52e-83) {
		tmp = ((c * (t * j)) + (x * (y * z))) - (b * (z * c));
	} else if (t <= 3.9e+102) {
		tmp = (y * ((x * z) - (i * j))) + t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-1.45d+138)) then
        tmp = t_2
    else if (t <= (-3.8d-39)) then
        tmp = t_1 - (j * ((y * i) - (t * c)))
    else if (t <= (-1.52d-83)) then
        tmp = ((c * (t * j)) + (x * (y * z))) - (b * (z * c))
    else if (t <= 3.9d+102) then
        tmp = (y * ((x * z) - (i * j))) + t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1.45e+138) {
		tmp = t_2;
	} else if (t <= -3.8e-39) {
		tmp = t_1 - (j * ((y * i) - (t * c)));
	} else if (t <= -1.52e-83) {
		tmp = ((c * (t * j)) + (x * (y * z))) - (b * (z * c));
	} else if (t <= 3.9e+102) {
		tmp = (y * ((x * z) - (i * j))) + t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -1.45e+138:
		tmp = t_2
	elif t <= -3.8e-39:
		tmp = t_1 - (j * ((y * i) - (t * c)))
	elif t <= -1.52e-83:
		tmp = ((c * (t * j)) + (x * (y * z))) - (b * (z * c))
	elif t <= 3.9e+102:
		tmp = (y * ((x * z) - (i * j))) + t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.45e+138)
		tmp = t_2;
	elseif (t <= -3.8e-39)
		tmp = Float64(t_1 - Float64(j * Float64(Float64(y * i) - Float64(t * c))));
	elseif (t <= -1.52e-83)
		tmp = Float64(Float64(Float64(c * Float64(t * j)) + Float64(x * Float64(y * z))) - Float64(b * Float64(z * c)));
	elseif (t <= 3.9e+102)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -1.45e+138)
		tmp = t_2;
	elseif (t <= -3.8e-39)
		tmp = t_1 - (j * ((y * i) - (t * c)));
	elseif (t <= -1.52e-83)
		tmp = ((c * (t * j)) + (x * (y * z))) - (b * (z * c));
	elseif (t <= 3.9e+102)
		tmp = (y * ((x * z) - (i * j))) + t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.45e+138], t$95$2, If[LessEqual[t, -3.8e-39], N[(t$95$1 - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.52e-83], N[(N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e+102], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.45000000000000005e138 or 3.8999999999999998e102 < t

   1. Initial program 59.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 72.2%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 72.2%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 72.2%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 72.2%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 72.2%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 72.2%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   5. Simplified 72.2%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]

   if -1.45000000000000005e138 < t < -3.8000000000000002e-39

   1. Initial program 85.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 75.4%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 75.4%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. *-commutative 75.4%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 75.4%

         \[\leadsto j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 75.4%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   if -3.8000000000000002e-39 < t < -1.51999999999999994e-83

   1. Initial program 83.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around 0 83.3%

      \[\leadsto \color{blue}{\left(c \cdot \left(j \cdot t\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - b \cdot \left(c \cdot z\right)} \]

   4. Taylor expanded in y around inf 83.3%

      \[\leadsto \left(c \cdot \left(j \cdot t\right) + \color{blue}{x \cdot \left(y \cdot z\right)}\right) - b \cdot \left(c \cdot z\right) \]

   if -1.51999999999999994e-83 < t < 3.8999999999999998e102

   1. Initial program 76.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 72.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 72.5%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 74.6%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 72.5%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 72.5%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 75.3%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 75.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 75.3%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 75.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 75.3%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 75.3%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+138}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-39}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;t \leq -1.52 \cdot 10^{-83}:\\ \;\;\;\;\left(c \cdot \left(t \cdot j\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+102}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 30.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{+56}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-308}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-29}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 7.6 \cdot 10^{+194}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* b (- c)))))
   (if (<= b -6.8e+106)
     t_1
     (if (<= b -7.2e+56)
       (* i (* a b))
       (if (<= b -2.5e+19)
         (* t (* c j))
         (if (<= b -3.8e-308)
           (* y (* x z))
           (if (<= b 1.5e-29)
             (* c (* t j))
             (if (<= b 7.6e+194) t_1 (* a (* b i))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (b * -c);
	double tmp;
	if (b <= -6.8e+106) {
		tmp = t_1;
	} else if (b <= -7.2e+56) {
		tmp = i * (a * b);
	} else if (b <= -2.5e+19) {
		tmp = t * (c * j);
	} else if (b <= -3.8e-308) {
		tmp = y * (x * z);
	} else if (b <= 1.5e-29) {
		tmp = c * (t * j);
	} else if (b <= 7.6e+194) {
		tmp = t_1;
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (b * -c)
    if (b <= (-6.8d+106)) then
        tmp = t_1
    else if (b <= (-7.2d+56)) then
        tmp = i * (a * b)
    else if (b <= (-2.5d+19)) then
        tmp = t * (c * j)
    else if (b <= (-3.8d-308)) then
        tmp = y * (x * z)
    else if (b <= 1.5d-29) then
        tmp = c * (t * j)
    else if (b <= 7.6d+194) then
        tmp = t_1
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (b * -c);
	double tmp;
	if (b <= -6.8e+106) {
		tmp = t_1;
	} else if (b <= -7.2e+56) {
		tmp = i * (a * b);
	} else if (b <= -2.5e+19) {
		tmp = t * (c * j);
	} else if (b <= -3.8e-308) {
		tmp = y * (x * z);
	} else if (b <= 1.5e-29) {
		tmp = c * (t * j);
	} else if (b <= 7.6e+194) {
		tmp = t_1;
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (b * -c)
	tmp = 0
	if b <= -6.8e+106:
		tmp = t_1
	elif b <= -7.2e+56:
		tmp = i * (a * b)
	elif b <= -2.5e+19:
		tmp = t * (c * j)
	elif b <= -3.8e-308:
		tmp = y * (x * z)
	elif b <= 1.5e-29:
		tmp = c * (t * j)
	elif b <= 7.6e+194:
		tmp = t_1
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(b * Float64(-c)))
	tmp = 0.0
	if (b <= -6.8e+106)
		tmp = t_1;
	elseif (b <= -7.2e+56)
		tmp = Float64(i * Float64(a * b));
	elseif (b <= -2.5e+19)
		tmp = Float64(t * Float64(c * j));
	elseif (b <= -3.8e-308)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= 1.5e-29)
		tmp = Float64(c * Float64(t * j));
	elseif (b <= 7.6e+194)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (b * -c);
	tmp = 0.0;
	if (b <= -6.8e+106)
		tmp = t_1;
	elseif (b <= -7.2e+56)
		tmp = i * (a * b);
	elseif (b <= -2.5e+19)
		tmp = t * (c * j);
	elseif (b <= -3.8e-308)
		tmp = y * (x * z);
	elseif (b <= 1.5e-29)
		tmp = c * (t * j);
	elseif (b <= 7.6e+194)
		tmp = t_1;
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.8e+106], t$95$1, If[LessEqual[b, -7.2e+56], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.5e+19], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.8e-308], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e-29], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.6e+194], t$95$1, N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -6.79999999999999989e106 or 1.5000000000000001e-29 < b < 7.5999999999999998e194

   1. Initial program 76.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 63.0%

      \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 63.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. associate-*r* 61.8%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right) \]

      3. associate-*r* 58.9%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right) \]

      4. distribute-rgt-out-- 58.9%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      5. +-commutative 58.9%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \]

      6. cancel-sign-sub-inv 58.9%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\left(c \cdot t + \left(-i\right) \cdot y\right)} \]

      7. *-commutative 58.9%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(\color{blue}{t \cdot c} + \left(-i\right) \cdot y\right) \]

      8. fma-udef 58.9%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)} \]

      9. fma-def 60.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, x \cdot y - b \cdot c, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right)} \]

      10. fma-neg 60.0%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(x, y, -b \cdot c\right)}, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      11. *-commutative 60.0%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, -\color{blue}{c \cdot b}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      12. distribute-rgt-neg-in 60.0%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, \color{blue}{c \cdot \left(-b\right)}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      13. distribute-lft-neg-out 60.0%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{-i \cdot y}\right)\right) \]

      14. distribute-rgt-neg-in 60.0%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{i \cdot \left(-y\right)}\right)\right) \]

   5. Simplified 60.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, i \cdot \left(-y\right)\right)\right)} \]

   6. Taylor expanded in b around inf 43.5%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 43.5%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

      2. *-commutative 43.5%

         \[\leadsto -b \cdot \color{blue}{\left(z \cdot c\right)} \]

      3. *-commutative 43.5%

         \[\leadsto -\color{blue}{\left(z \cdot c\right) \cdot b} \]

      4. associate-*l* 42.8%

         \[\leadsto -\color{blue}{z \cdot \left(c \cdot b\right)} \]

   8. Simplified 42.8%

      \[\leadsto \color{blue}{-z \cdot \left(c \cdot b\right)} \]

   if -6.79999999999999989e106 < b < -7.19999999999999996e56

   1. Initial program 81.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 81.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 81.1%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 81.2%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 68.8%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 68.8%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 68.8%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 68.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 68.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 68.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 68.8%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 68.8%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in a around inf 46.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 46.2%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} \]

      2. *-commutative 46.2%

         \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot a \]

      3. associate-*l* 57.6%

         \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} \]

   8. Simplified 57.6%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} \]

   if -7.19999999999999996e56 < b < -2.5e19

   1. Initial program 99.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 48.0%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.0%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 48.0%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 48.0%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 48.0%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 48.0%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   5. Simplified 48.0%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]

   6. Taylor expanded in j around inf 47.8%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-commutative 47.8%

         \[\leadsto t \cdot \color{blue}{\left(j \cdot c\right)} \]

   8. Simplified 47.8%

      \[\leadsto t \cdot \color{blue}{\left(j \cdot c\right)} \]

   if -2.5e19 < b < -3.79999999999999975e-308

   1. Initial program 69.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 57.8%

      \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 57.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. associate-*r* 64.7%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right) \]

      3. associate-*r* 66.2%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right) \]

      4. distribute-rgt-out-- 66.2%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      5. +-commutative 66.2%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \]

      6. cancel-sign-sub-inv 66.2%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\left(c \cdot t + \left(-i\right) \cdot y\right)} \]

      7. *-commutative 66.2%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(\color{blue}{t \cdot c} + \left(-i\right) \cdot y\right) \]

      8. fma-udef 66.2%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)} \]

      9. fma-def 69.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, x \cdot y - b \cdot c, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right)} \]

      10. fma-neg 69.4%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(x, y, -b \cdot c\right)}, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      11. *-commutative 69.4%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, -\color{blue}{c \cdot b}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      12. distribute-rgt-neg-in 69.4%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, \color{blue}{c \cdot \left(-b\right)}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      13. distribute-lft-neg-out 69.4%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{-i \cdot y}\right)\right) \]

      14. distribute-rgt-neg-in 69.4%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{i \cdot \left(-y\right)}\right)\right) \]

   5. Simplified 69.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, i \cdot \left(-y\right)\right)\right)} \]

   6. Taylor expanded in x around inf 30.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 30.8%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. associate-*l* 33.8%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   8. Simplified 33.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -3.79999999999999975e-308 < b < 1.5000000000000001e-29

   1. Initial program 64.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 47.3%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 47.3%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 47.3%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 47.3%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 47.3%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 47.3%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   5. Simplified 47.3%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]

   6. Taylor expanded in j around inf 28.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if 7.5999999999999998e194 < b

   1. Initial program 68.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 70.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 70.5%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 70.7%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 75.0%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 75.0%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 75.0%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 75.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 75.0%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 75.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 75.0%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 75.0%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in a around inf 52.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 52.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

   8. Simplified 52.5%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+106}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{+56}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-308}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-29}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 7.6 \cdot 10^{+194}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-72}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* c (* t j)) (* b (- (* a i) (* z c)))))
        (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -1.1e+50)
     t_2
     (if (<= y 1.25e-99)
       t_1
       (if (<= y 1.65e-72) (* t (* x (- a))) (if (<= y 1.16e+72) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (c * (t * j)) + (b * ((a * i) - (z * c)));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.1e+50) {
		tmp = t_2;
	} else if (y <= 1.25e-99) {
		tmp = t_1;
	} else if (y <= 1.65e-72) {
		tmp = t * (x * -a);
	} else if (y <= 1.16e+72) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (c * (t * j)) + (b * ((a * i) - (z * c)))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-1.1d+50)) then
        tmp = t_2
    else if (y <= 1.25d-99) then
        tmp = t_1
    else if (y <= 1.65d-72) then
        tmp = t * (x * -a)
    else if (y <= 1.16d+72) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (c * (t * j)) + (b * ((a * i) - (z * c)));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.1e+50) {
		tmp = t_2;
	} else if (y <= 1.25e-99) {
		tmp = t_1;
	} else if (y <= 1.65e-72) {
		tmp = t * (x * -a);
	} else if (y <= 1.16e+72) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (c * (t * j)) + (b * ((a * i) - (z * c)))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.1e+50:
		tmp = t_2
	elif y <= 1.25e-99:
		tmp = t_1
	elif y <= 1.65e-72:
		tmp = t * (x * -a)
	elif y <= 1.16e+72:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(c * Float64(t * j)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.1e+50)
		tmp = t_2;
	elseif (y <= 1.25e-99)
		tmp = t_1;
	elseif (y <= 1.65e-72)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (y <= 1.16e+72)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (c * (t * j)) + (b * ((a * i) - (z * c)));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.1e+50)
		tmp = t_2;
	elseif (y <= 1.25e-99)
		tmp = t_1;
	elseif (y <= 1.65e-72)
		tmp = t * (x * -a);
	elseif (y <= 1.16e+72)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e+50], t$95$2, If[LessEqual[y, 1.25e-99], t$95$1, If[LessEqual[y, 1.65e-72], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.16e+72], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.10000000000000008e50 or 1.16000000000000003e72 < y

   1. Initial program 64.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 70.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 70.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 70.7%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 70.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

   5. Simplified 70.7%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right)} \]

   if -1.10000000000000008e50 < y < 1.24999999999999992e-99 or 1.65e-72 < y < 1.16000000000000003e72

   1. Initial program 80.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 63.8%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 63.8%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. *-commutative 63.8%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 63.8%

         \[\leadsto j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 63.8%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in y around 0 64.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 64.0%

         \[\leadsto c \cdot \left(j \cdot t\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

      2. *-commutative 64.0%

         \[\leadsto c \cdot \left(j \cdot t\right) - b \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right) \]

   8. Simplified 64.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right) - b \cdot \left(z \cdot c - i \cdot a\right)} \]

   if 1.24999999999999992e-99 < y < 1.65e-72

   1. Initial program 71.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 71.9%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 71.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 71.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 71.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 71.9%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 71.9%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   5. Simplified 71.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]

   6. Taylor expanded in j around 0 71.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 71.8%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} \]

      2. neg-mul-1 71.8%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) \]

      3. *-commutative 71.8%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(x \cdot t\right)} \]

      4. associate-*r* 72.2%

         \[\leadsto \color{blue}{\left(\left(-a\right) \cdot x\right) \cdot t} \]

      5. distribute-lft-neg-in 72.2%

         \[\leadsto \color{blue}{\left(-a \cdot x\right)} \cdot t \]

      6. *-commutative 72.2%

         \[\leadsto \left(-\color{blue}{x \cdot a}\right) \cdot t \]

      7. distribute-rgt-neg-in 72.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(-a\right)\right)} \cdot t \]

   8. Simplified 72.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(-a\right)\right) \cdot t} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-99}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-72}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+72}:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+138}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 0.00084:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y (- (* x z) (* i j))) (* z (* b c))))
        (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -1e+138)
     t_2
     (if (<= t 1.65e-71)
       t_1
       (if (<= t 0.00084)
         (+ (* c (* t j)) (* b (- (* a i) (* z c))))
         (if (<= t 8.2e+105) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) - (z * (b * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1e+138) {
		tmp = t_2;
	} else if (t <= 1.65e-71) {
		tmp = t_1;
	} else if (t <= 0.00084) {
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)));
	} else if (t <= 8.2e+105) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * ((x * z) - (i * j))) - (z * (b * c))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-1d+138)) then
        tmp = t_2
    else if (t <= 1.65d-71) then
        tmp = t_1
    else if (t <= 0.00084d0) then
        tmp = (c * (t * j)) + (b * ((a * i) - (z * c)))
    else if (t <= 8.2d+105) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) - (z * (b * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1e+138) {
		tmp = t_2;
	} else if (t <= 1.65e-71) {
		tmp = t_1;
	} else if (t <= 0.00084) {
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)));
	} else if (t <= 8.2e+105) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * ((x * z) - (i * j))) - (z * (b * c))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -1e+138:
		tmp = t_2
	elif t <= 1.65e-71:
		tmp = t_1
	elif t <= 0.00084:
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)))
	elif t <= 8.2e+105:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(z * Float64(b * c)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1e+138)
		tmp = t_2;
	elseif (t <= 1.65e-71)
		tmp = t_1;
	elseif (t <= 0.00084)
		tmp = Float64(Float64(c * Float64(t * j)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (t <= 8.2e+105)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * ((x * z) - (i * j))) - (z * (b * c));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -1e+138)
		tmp = t_2;
	elseif (t <= 1.65e-71)
		tmp = t_1;
	elseif (t <= 0.00084)
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)));
	elseif (t <= 8.2e+105)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e+138], t$95$2, If[LessEqual[t, 1.65e-71], t$95$1, If[LessEqual[t, 0.00084], N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e+105], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1e138 or 8.2000000000000005e105 < t

   1. Initial program 59.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 72.2%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 72.2%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 72.2%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 72.2%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 72.2%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 72.2%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   5. Simplified 72.2%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]

   if -1e138 < t < 1.6500000000000001e-71 or 8.4000000000000003e-4 < t < 8.2000000000000005e105

   1. Initial program 78.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 70.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 70.6%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 71.3%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 70.6%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 70.6%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 73.1%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 73.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 73.1%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 73.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 73.1%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 73.1%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in z around inf 67.5%

      \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - \color{blue}{b \cdot \left(c \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 67.5%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \color{blue}{\left(z \cdot c\right)} \]

      2. *-commutative 67.5%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - \color{blue}{\left(z \cdot c\right) \cdot b} \]

      3. associate-*l* 67.6%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - \color{blue}{z \cdot \left(c \cdot b\right)} \]

      4. *-commutative 67.6%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \color{blue}{\left(b \cdot c\right)} \]

   8. Simplified 67.6%

      \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - \color{blue}{z \cdot \left(b \cdot c\right)} \]

   if 1.6500000000000001e-71 < t < 8.4000000000000003e-4

   1. Initial program 74.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.1%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 81.1%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. *-commutative 81.1%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 81.1%

         \[\leadsto j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 81.1%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in y around 0 75.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 75.5%

         \[\leadsto c \cdot \left(j \cdot t\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

      2. *-commutative 75.5%

         \[\leadsto c \cdot \left(j \cdot t\right) - b \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right) \]

   8. Simplified 75.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right) - b \cdot \left(z \cdot c - i \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+138}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-71}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;t \leq 0.00084:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+105}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{-103}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 0.000195:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y (- (* x z) (* i j))) (* z (* b c)))))
   (if (<= t -6.8e-103)
     (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a))))
     (if (<= t 8.5e-72)
       t_1
       (if (<= t 0.000195)
         (+ (* c (* t j)) (* b (- (* a i) (* z c))))
         (if (<= t 1.18e+106) t_1 (* t (- (* c j) (* x a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) - (z * (b * c));
	double tmp;
	if (t <= -6.8e-103) {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else if (t <= 8.5e-72) {
		tmp = t_1;
	} else if (t <= 0.000195) {
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)));
	} else if (t <= 1.18e+106) {
		tmp = t_1;
	} else {
		tmp = t * ((c * j) - (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * ((x * z) - (i * j))) - (z * (b * c))
    if (t <= (-6.8d-103)) then
        tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else if (t <= 8.5d-72) then
        tmp = t_1
    else if (t <= 0.000195d0) then
        tmp = (c * (t * j)) + (b * ((a * i) - (z * c)))
    else if (t <= 1.18d+106) then
        tmp = t_1
    else
        tmp = t * ((c * j) - (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) - (z * (b * c));
	double tmp;
	if (t <= -6.8e-103) {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else if (t <= 8.5e-72) {
		tmp = t_1;
	} else if (t <= 0.000195) {
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)));
	} else if (t <= 1.18e+106) {
		tmp = t_1;
	} else {
		tmp = t * ((c * j) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * ((x * z) - (i * j))) - (z * (b * c))
	tmp = 0
	if t <= -6.8e-103:
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	elif t <= 8.5e-72:
		tmp = t_1
	elif t <= 0.000195:
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)))
	elif t <= 1.18e+106:
		tmp = t_1
	else:
		tmp = t * ((c * j) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(z * Float64(b * c)))
	tmp = 0.0
	if (t <= -6.8e-103)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	elseif (t <= 8.5e-72)
		tmp = t_1;
	elseif (t <= 0.000195)
		tmp = Float64(Float64(c * Float64(t * j)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (t <= 1.18e+106)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * ((x * z) - (i * j))) - (z * (b * c));
	tmp = 0.0;
	if (t <= -6.8e-103)
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	elseif (t <= 8.5e-72)
		tmp = t_1;
	elseif (t <= 0.000195)
		tmp = (c * (t * j)) + (b * ((a * i) - (z * c)));
	elseif (t <= 1.18e+106)
		tmp = t_1;
	else
		tmp = t * ((c * j) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e-103], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-72], t$95$1, If[LessEqual[t, 0.000195], N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.18e+106], t$95$1, N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.80000000000000006e-103

   1. Initial program 74.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 62.2%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   if -6.80000000000000006e-103 < t < 8.50000000000000008e-72 or 1.94999999999999996e-4 < t < 1.17999999999999993e106

   1. Initial program 76.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 72.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 72.6%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 74.3%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 74.3%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 74.3%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 77.6%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 77.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 77.6%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 77.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 77.6%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 77.6%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in z around inf 72.4%

      \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - \color{blue}{b \cdot \left(c \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 72.4%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \color{blue}{\left(z \cdot c\right)} \]

      2. *-commutative 72.4%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - \color{blue}{\left(z \cdot c\right) \cdot b} \]

      3. associate-*l* 73.4%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - \color{blue}{z \cdot \left(c \cdot b\right)} \]

      4. *-commutative 73.4%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \color{blue}{\left(b \cdot c\right)} \]

   8. Simplified 73.4%

      \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - \color{blue}{z \cdot \left(b \cdot c\right)} \]

   if 8.50000000000000008e-72 < t < 1.94999999999999996e-4

   1. Initial program 74.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.1%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 81.1%

         \[\leadsto j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. *-commutative 81.1%

         \[\leadsto j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. *-commutative 81.1%

         \[\leadsto j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 81.1%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in y around 0 75.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 75.5%

         \[\leadsto c \cdot \left(j \cdot t\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

      2. *-commutative 75.5%

         \[\leadsto c \cdot \left(j \cdot t\right) - b \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right) \]

   8. Simplified 75.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right) - b \cdot \left(z \cdot c - i \cdot a\right)} \]

   if 1.17999999999999993e106 < t

   1. Initial program 58.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 76.9%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 76.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 76.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 76.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 76.9%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 76.9%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   5. Simplified 76.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{-103}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-72}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;t \leq 0.000195:\\ \;\;\;\;c \cdot \left(t \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{+106}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 41.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+50}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-72}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= y -3.6e+50)
     (* i (* y (- j)))
     (if (<= y 1.32e-117)
       t_1
       (if (<= y 1.65e-72)
         (* a (* t (- x)))
         (if (<= y 1.8e+106) t_1 (* (* i j) (- y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (y <= -3.6e+50) {
		tmp = i * (y * -j);
	} else if (y <= 1.32e-117) {
		tmp = t_1;
	} else if (y <= 1.65e-72) {
		tmp = a * (t * -x);
	} else if (y <= 1.8e+106) {
		tmp = t_1;
	} else {
		tmp = (i * j) * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    if (y <= (-3.6d+50)) then
        tmp = i * (y * -j)
    else if (y <= 1.32d-117) then
        tmp = t_1
    else if (y <= 1.65d-72) then
        tmp = a * (t * -x)
    else if (y <= 1.8d+106) then
        tmp = t_1
    else
        tmp = (i * j) * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double tmp;
	if (y <= -3.6e+50) {
		tmp = i * (y * -j);
	} else if (y <= 1.32e-117) {
		tmp = t_1;
	} else if (y <= 1.65e-72) {
		tmp = a * (t * -x);
	} else if (y <= 1.8e+106) {
		tmp = t_1;
	} else {
		tmp = (i * j) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if y <= -3.6e+50:
		tmp = i * (y * -j)
	elif y <= 1.32e-117:
		tmp = t_1
	elif y <= 1.65e-72:
		tmp = a * (t * -x)
	elif y <= 1.8e+106:
		tmp = t_1
	else:
		tmp = (i * j) * -y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (y <= -3.6e+50)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (y <= 1.32e-117)
		tmp = t_1;
	elseif (y <= 1.65e-72)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (y <= 1.8e+106)
		tmp = t_1;
	else
		tmp = Float64(Float64(i * j) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (y <= -3.6e+50)
		tmp = i * (y * -j);
	elseif (y <= 1.32e-117)
		tmp = t_1;
	elseif (y <= 1.65e-72)
		tmp = a * (t * -x);
	elseif (y <= 1.8e+106)
		tmp = t_1;
	else
		tmp = (i * j) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+50], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.32e-117], t$95$1, If[LessEqual[y, 1.65e-72], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+106], t$95$1, N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.59999999999999986e50

   1. Initial program 63.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 43.7%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   4. Taylor expanded in c around 0 42.4%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 42.4%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

      2. neg-mul-1 42.4%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

      3. *-commutative 42.4%

         \[\leadsto \left(-i\right) \cdot \color{blue}{\left(y \cdot j\right)} \]

   6. Simplified 42.4%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   if -3.59999999999999986e50 < y < 1.32e-117 or 1.65e-72 < y < 1.8e106

   1. Initial program 80.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 51.5%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 51.5%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 51.5%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   if 1.32e-117 < y < 1.65e-72

   1. Initial program 74.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 75.4%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 75.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 75.4%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 75.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 75.4%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 75.4%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   5. Simplified 75.4%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]

   6. Taylor expanded in j around 0 75.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 75.3%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} \]

      2. neg-mul-1 75.3%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) \]

      3. *-commutative 75.3%

         \[\leadsto \left(-a\right) \cdot \color{blue}{\left(x \cdot t\right)} \]

   8. Simplified 75.3%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot t\right)} \]

   if 1.8e106 < y

   1. Initial program 64.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 66.5%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   4. Taylor expanded in c around 0 53.3%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 57.0%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} \]

      2. associate-*r* 57.0%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} \]

      3. *-commutative 57.0%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg 57.0%

         \[\leadsto y \cdot \color{blue}{\left(-i \cdot j\right)} \]

      5. *-commutative 57.0%

         \[\leadsto y \cdot \left(-\color{blue}{j \cdot i}\right) \]

      6. distribute-rgt-neg-in 57.0%

         \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   6. Simplified 57.0%

      \[\leadsto \color{blue}{y \cdot \left(j \cdot \left(-i\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+50}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-117}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-72}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+106}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot \left(-c\right)\right)\\ t_2 := \left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-267}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* b (- c)))) (t_2 (* (* i j) (- y))))
   (if (<= y -1.02e+36)
     t_2
     (if (<= y -4.1e-193)
       t_1
       (if (<= y 1.3e-267) (* i (* a b)) (if (<= y 1.8e+52) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (b * -c);
	double t_2 = (i * j) * -y;
	double tmp;
	if (y <= -1.02e+36) {
		tmp = t_2;
	} else if (y <= -4.1e-193) {
		tmp = t_1;
	} else if (y <= 1.3e-267) {
		tmp = i * (a * b);
	} else if (y <= 1.8e+52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (b * -c)
    t_2 = (i * j) * -y
    if (y <= (-1.02d+36)) then
        tmp = t_2
    else if (y <= (-4.1d-193)) then
        tmp = t_1
    else if (y <= 1.3d-267) then
        tmp = i * (a * b)
    else if (y <= 1.8d+52) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (b * -c);
	double t_2 = (i * j) * -y;
	double tmp;
	if (y <= -1.02e+36) {
		tmp = t_2;
	} else if (y <= -4.1e-193) {
		tmp = t_1;
	} else if (y <= 1.3e-267) {
		tmp = i * (a * b);
	} else if (y <= 1.8e+52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (b * -c)
	t_2 = (i * j) * -y
	tmp = 0
	if y <= -1.02e+36:
		tmp = t_2
	elif y <= -4.1e-193:
		tmp = t_1
	elif y <= 1.3e-267:
		tmp = i * (a * b)
	elif y <= 1.8e+52:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(b * Float64(-c)))
	t_2 = Float64(Float64(i * j) * Float64(-y))
	tmp = 0.0
	if (y <= -1.02e+36)
		tmp = t_2;
	elseif (y <= -4.1e-193)
		tmp = t_1;
	elseif (y <= 1.3e-267)
		tmp = Float64(i * Float64(a * b));
	elseif (y <= 1.8e+52)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (b * -c);
	t_2 = (i * j) * -y;
	tmp = 0.0;
	if (y <= -1.02e+36)
		tmp = t_2;
	elseif (y <= -4.1e-193)
		tmp = t_1;
	elseif (y <= 1.3e-267)
		tmp = i * (a * b);
	elseif (y <= 1.8e+52)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision]}, If[LessEqual[y, -1.02e+36], t$95$2, If[LessEqual[y, -4.1e-193], t$95$1, If[LessEqual[y, 1.3e-267], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+52], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.02000000000000003e36 or 1.8e52 < y

   1. Initial program 65.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 51.9%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   4. Taylor expanded in c around 0 44.8%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 46.4%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} \]

      2. associate-*r* 46.4%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} \]

      3. *-commutative 46.4%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg 46.4%

         \[\leadsto y \cdot \color{blue}{\left(-i \cdot j\right)} \]

      5. *-commutative 46.4%

         \[\leadsto y \cdot \left(-\color{blue}{j \cdot i}\right) \]

      6. distribute-rgt-neg-in 46.4%

         \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   6. Simplified 46.4%

      \[\leadsto \color{blue}{y \cdot \left(j \cdot \left(-i\right)\right)} \]

   if -1.02000000000000003e36 < y < -4.10000000000000003e-193 or 1.3000000000000001e-267 < y < 1.8e52

   1. Initial program 80.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 56.5%

      \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 56.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. associate-*r* 56.5%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right) \]

      3. associate-*r* 58.4%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right) \]

      4. distribute-rgt-out-- 58.4%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      5. +-commutative 58.4%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \]

      6. cancel-sign-sub-inv 58.4%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\left(c \cdot t + \left(-i\right) \cdot y\right)} \]

      7. *-commutative 58.4%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(\color{blue}{t \cdot c} + \left(-i\right) \cdot y\right) \]

      8. fma-udef 58.4%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)} \]

      9. fma-def 58.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, x \cdot y - b \cdot c, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right)} \]

      10. fma-neg 58.4%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(x, y, -b \cdot c\right)}, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      11. *-commutative 58.4%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, -\color{blue}{c \cdot b}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      12. distribute-rgt-neg-in 58.4%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, \color{blue}{c \cdot \left(-b\right)}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      13. distribute-lft-neg-out 58.4%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{-i \cdot y}\right)\right) \]

      14. distribute-rgt-neg-in 58.4%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{i \cdot \left(-y\right)}\right)\right) \]

   5. Simplified 58.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, i \cdot \left(-y\right)\right)\right)} \]

   6. Taylor expanded in b around inf 35.6%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 35.6%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

      2. *-commutative 35.6%

         \[\leadsto -b \cdot \color{blue}{\left(z \cdot c\right)} \]

      3. *-commutative 35.6%

         \[\leadsto -\color{blue}{\left(z \cdot c\right) \cdot b} \]

      4. associate-*l* 34.0%

         \[\leadsto -\color{blue}{z \cdot \left(c \cdot b\right)} \]

   8. Simplified 34.0%

      \[\leadsto \color{blue}{-z \cdot \left(c \cdot b\right)} \]

   if -4.10000000000000003e-193 < y < 1.3000000000000001e-267

   1. Initial program 73.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 57.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 57.0%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 53.1%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 44.5%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 44.5%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 44.5%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 44.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 44.5%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 44.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 44.5%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 44.5%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in a around inf 45.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 45.1%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} \]

      2. *-commutative 45.1%

         \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot a \]

      3. associate-*l* 49.2%

         \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} \]

   8. Simplified 49.2%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+36}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-193}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-267}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+52}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-70} \lor \neg \left(z \leq 6.8\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -3e-70) (not (<= z 6.8))) (* x (* y z)) (* b (* a i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -3e-70) || !(z <= 6.8)) {
		tmp = x * (y * z);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((z <= (-3d-70)) .or. (.not. (z <= 6.8d0))) then
        tmp = x * (y * z)
    else
        tmp = b * (a * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -3e-70) || !(z <= 6.8)) {
		tmp = x * (y * z);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -3e-70) or not (z <= 6.8):
		tmp = x * (y * z)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -3e-70) || !(z <= 6.8))
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -3e-70) || ~((z <= 6.8)))
		tmp = x * (y * z);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -3e-70], N[Not[LessEqual[z, 6.8]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.0000000000000001e-70 or 6.79999999999999982 < z

   1. Initial program 66.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 63.8%

      \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 63.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. associate-*r* 68.7%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right) \]

      3. associate-*r* 70.8%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right) \]

      4. distribute-rgt-out-- 71.6%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      5. +-commutative 71.6%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \]

      6. cancel-sign-sub-inv 71.6%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\left(c \cdot t + \left(-i\right) \cdot y\right)} \]

      7. *-commutative 71.6%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(\color{blue}{t \cdot c} + \left(-i\right) \cdot y\right) \]

      8. fma-udef 71.6%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)} \]

      9. fma-def 73.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, x \cdot y - b \cdot c, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right)} \]

      10. fma-neg 73.9%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(x, y, -b \cdot c\right)}, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      11. *-commutative 73.9%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, -\color{blue}{c \cdot b}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      12. distribute-rgt-neg-in 73.9%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, \color{blue}{c \cdot \left(-b\right)}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      13. distribute-lft-neg-out 73.9%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{-i \cdot y}\right)\right) \]

      14. distribute-rgt-neg-in 73.9%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{i \cdot \left(-y\right)}\right)\right) \]

   5. Simplified 73.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, i \cdot \left(-y\right)\right)\right)} \]

   6. Taylor expanded in x around inf 37.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if -3.0000000000000001e-70 < z < 6.79999999999999982

   1. Initial program 79.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 35.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 35.3%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 35.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 27.1%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 27.1%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   8. Simplified 27.1%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-70} \lor \neg \left(z \leq 6.8\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{-106}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-11}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.06e-106)
   (* a (* b i))
   (if (<= a 3.9e-11) (* c (* t j)) (* b (* a i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.06e-106) {
		tmp = a * (b * i);
	} else if (a <= 3.9e-11) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-1.06d-106)) then
        tmp = a * (b * i)
    else if (a <= 3.9d-11) then
        tmp = c * (t * j)
    else
        tmp = b * (a * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.06e-106) {
		tmp = a * (b * i);
	} else if (a <= 3.9e-11) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.06e-106:
		tmp = a * (b * i)
	elif a <= 3.9e-11:
		tmp = c * (t * j)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.06e-106)
		tmp = Float64(a * Float64(b * i));
	elseif (a <= 3.9e-11)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.06e-106)
		tmp = a * (b * i);
	elseif (a <= 3.9e-11)
		tmp = c * (t * j);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.06e-106], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.9e-11], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.06e-106

   1. Initial program 67.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 50.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 50.2%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 51.5%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 50.2%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 50.2%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 51.5%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 51.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 51.5%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 51.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 51.5%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 51.5%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in a around inf 26.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 26.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

   8. Simplified 26.8%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   if -1.06e-106 < a < 3.9000000000000001e-11

   1. Initial program 82.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 31.7%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 31.7%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 31.7%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 31.7%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 31.7%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 31.7%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   5. Simplified 31.7%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]

   6. Taylor expanded in j around inf 25.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if 3.9000000000000001e-11 < a

   1. Initial program 61.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 52.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 52.1%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 52.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 39.7%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.7%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   8. Simplified 39.7%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 29.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{-106}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-11}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+58}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+55}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -5.8e+58)
   (* i (* a b))
   (if (<= b 7.8e+55) (* c (* t j)) (* a (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -5.8e+58) {
		tmp = i * (a * b);
	} else if (b <= 7.8e+55) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-5.8d+58)) then
        tmp = i * (a * b)
    else if (b <= 7.8d+55) then
        tmp = c * (t * j)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -5.8e+58) {
		tmp = i * (a * b);
	} else if (b <= 7.8e+55) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -5.8e+58:
		tmp = i * (a * b)
	elif b <= 7.8e+55:
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -5.8e+58)
		tmp = Float64(i * Float64(a * b));
	elseif (b <= 7.8e+55)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -5.8e+58)
		tmp = i * (a * b);
	elseif (b <= 7.8e+55)
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -5.8e+58], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.8e+55], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.80000000000000004e58

   1. Initial program 81.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 77.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 77.3%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 75.5%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 68.0%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 68.0%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 69.9%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 69.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 69.9%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 69.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 69.9%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 69.9%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in a around inf 37.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 37.5%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} \]

      2. *-commutative 37.5%

         \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot a \]

      3. associate-*l* 41.1%

         \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} \]

   8. Simplified 41.1%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} \]

   if -5.80000000000000004e58 < b < 7.80000000000000054e55

   1. Initial program 71.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 38.5%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 38.5%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 38.5%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 38.5%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 38.5%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 38.5%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   5. Simplified 38.5%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]

   6. Taylor expanded in j around inf 22.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if 7.80000000000000054e55 < b

   1. Initial program 69.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 73.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 73.3%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 73.4%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 75.1%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 75.1%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 76.8%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 76.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 76.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 76.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 76.8%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 76.8%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in a around inf 37.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 37.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

   8. Simplified 37.8%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 29.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+58}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+55}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-117}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 10^{-8}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -2.4e-117)
   (* i (* a b))
   (if (<= a 1e-8) (* t (* c j)) (* b (* a i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -2.4e-117) {
		tmp = i * (a * b);
	} else if (a <= 1e-8) {
		tmp = t * (c * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-2.4d-117)) then
        tmp = i * (a * b)
    else if (a <= 1d-8) then
        tmp = t * (c * j)
    else
        tmp = b * (a * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -2.4e-117) {
		tmp = i * (a * b);
	} else if (a <= 1e-8) {
		tmp = t * (c * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -2.4e-117:
		tmp = i * (a * b)
	elif a <= 1e-8:
		tmp = t * (c * j)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -2.4e-117)
		tmp = Float64(i * Float64(a * b));
	elseif (a <= 1e-8)
		tmp = Float64(t * Float64(c * j));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -2.4e-117)
		tmp = i * (a * b);
	elseif (a <= 1e-8)
		tmp = t * (c * j);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -2.4e-117], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e-8], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.40000000000000014e-117

   1. Initial program 67.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 50.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 50.2%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 51.5%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 50.2%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 50.2%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 51.5%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 51.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 51.5%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 51.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 51.5%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 51.5%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in a around inf 26.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 26.8%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot a} \]

      2. *-commutative 26.8%

         \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot a \]

      3. associate-*l* 26.9%

         \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} \]

   8. Simplified 26.9%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} \]

   if -2.40000000000000014e-117 < a < 1e-8

   1. Initial program 82.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 31.7%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 31.7%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 31.7%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 31.7%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 31.7%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 31.7%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   5. Simplified 31.7%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]

   6. Taylor expanded in j around inf 26.5%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-commutative 26.5%

         \[\leadsto t \cdot \color{blue}{\left(j \cdot c\right)} \]

   8. Simplified 26.5%

      \[\leadsto t \cdot \color{blue}{\left(j \cdot c\right)} \]

   if 1e-8 < a

   1. Initial program 61.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 52.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 52.1%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 52.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 39.7%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.7%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   8. Simplified 39.7%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 29.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-117}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 10^{-8}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 12.2:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -3.5e-68)
   (* x (* y z))
   (if (<= z 12.2) (* b (* a i)) (* y (* x z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -3.5e-68) {
		tmp = x * (y * z);
	} else if (z <= 12.2) {
		tmp = b * (a * i);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-3.5d-68)) then
        tmp = x * (y * z)
    else if (z <= 12.2d0) then
        tmp = b * (a * i)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -3.5e-68) {
		tmp = x * (y * z);
	} else if (z <= 12.2) {
		tmp = b * (a * i);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -3.5e-68:
		tmp = x * (y * z)
	elif z <= 12.2:
		tmp = b * (a * i)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -3.5e-68)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 12.2)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -3.5e-68)
		tmp = x * (y * z);
	elseif (z <= 12.2)
		tmp = b * (a * i);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -3.5e-68], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 12.2], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.50000000000000013e-68

   1. Initial program 69.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 61.8%

      \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 61.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. associate-*r* 64.2%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right) \]

      3. associate-*r* 64.2%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right) \]

      4. distribute-rgt-out-- 65.6%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      5. +-commutative 65.6%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \]

      6. cancel-sign-sub-inv 65.6%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\left(c \cdot t + \left(-i\right) \cdot y\right)} \]

      7. *-commutative 65.6%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(\color{blue}{t \cdot c} + \left(-i\right) \cdot y\right) \]

      8. fma-udef 65.6%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)} \]

      9. fma-def 68.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, x \cdot y - b \cdot c, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right)} \]

      10. fma-neg 68.5%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(x, y, -b \cdot c\right)}, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      11. *-commutative 68.5%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, -\color{blue}{c \cdot b}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      12. distribute-rgt-neg-in 68.5%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, \color{blue}{c \cdot \left(-b\right)}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      13. distribute-lft-neg-out 68.5%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{-i \cdot y}\right)\right) \]

      14. distribute-rgt-neg-in 68.5%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{i \cdot \left(-y\right)}\right)\right) \]

   5. Simplified 68.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, i \cdot \left(-y\right)\right)\right)} \]

   6. Taylor expanded in x around inf 36.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if -3.50000000000000013e-68 < z < 12.199999999999999

   1. Initial program 79.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 35.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 35.3%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 35.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 27.1%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 27.1%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   8. Simplified 27.1%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   if 12.199999999999999 < z

   1. Initial program 62.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 66.0%

      \[\leadsto \color{blue}{\left(j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 66.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)\right)} \]

      2. associate-*r* 73.5%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\color{blue}{\left(x \cdot y\right) \cdot z} - b \cdot \left(c \cdot z\right)\right) \]

      3. associate-*r* 78.1%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \left(\left(x \cdot y\right) \cdot z - \color{blue}{\left(b \cdot c\right) \cdot z}\right) \]

      4. distribute-rgt-out-- 78.1%

         \[\leadsto j \cdot \left(c \cdot t - i \cdot y\right) + \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

      5. +-commutative 78.1%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \]

      6. cancel-sign-sub-inv 78.1%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\left(c \cdot t + \left(-i\right) \cdot y\right)} \]

      7. *-commutative 78.1%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \left(\color{blue}{t \cdot c} + \left(-i\right) \cdot y\right) \]

      8. fma-udef 78.1%

         \[\leadsto z \cdot \left(x \cdot y - b \cdot c\right) + j \cdot \color{blue}{\mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)} \]

      9. fma-def 79.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z, x \cdot y - b \cdot c, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right)} \]

      10. fma-neg 79.6%

          \[\leadsto \mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(x, y, -b \cdot c\right)}, j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      11. *-commutative 79.6%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, -\color{blue}{c \cdot b}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      12. distribute-rgt-neg-in 79.6%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, \color{blue}{c \cdot \left(-b\right)}\right), j \cdot \mathsf{fma}\left(t, c, \left(-i\right) \cdot y\right)\right) \]

      13. distribute-lft-neg-out 79.6%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{-i \cdot y}\right)\right) \]

      14. distribute-rgt-neg-in 79.6%

          \[\leadsto \mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, \color{blue}{i \cdot \left(-y\right)}\right)\right) \]

   5. Simplified 79.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z, \mathsf{fma}\left(x, y, c \cdot \left(-b\right)\right), j \cdot \mathsf{fma}\left(t, c, i \cdot \left(-y\right)\right)\right)} \]

   6. Taylor expanded in x around inf 39.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.2%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. associate-*l* 40.6%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   8. Simplified 40.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 33.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 12.2:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 22.5% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (b * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 72.7%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in t around 0 61.4%

   \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
4. Step-by-step derivation

   1. *-commutative 61.4%

      \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   2. associate-*r* 62.6%

      \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   3. associate-*r* 61.7%

      \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   4. associate-*r* 61.7%

      \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   5. distribute-rgt-in 64.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

   6. +-commutative 64.5%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

   7. mul-1-neg 64.5%

      \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   8. unsub-neg 64.5%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

   9. *-commutative 64.5%

      \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

5. Simplified 64.5%

   \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

6. Taylor expanded in a around inf 20.6%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
7. Step-by-step derivation

   1. *-commutative 20.6%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

8. Simplified 20.6%

   \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

9. Final simplification 20.6%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
10. Add Preprocessing

Developer target: 69.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024027 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))